I was wondering if I could get a hint on checking the convergence of the following integral $$\int_1^\infty \ln\left(1+\frac{\sin x}{\sqrt x}\right) \, dx $$ I managed to prove the it does not converge absolutely, but got stuck on checking if it converges conditionally. Thanks in advance.
2026-04-25 00:10:34.1777075834
Checking convergence of an integral.
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